We present an integral equation method for solving boundary value
problems of the Helmholtz equation in unbounded domains. The
method relies on the factorisation of one of the
Calderón projectors by an operator approximating the exterior
admittance (Dirichlet to Neumann) operator of the scattering
obstacle. We show how the pseudo-differential calculus allows us
to construct such approximations and that this yields integral
equations without internal resonances and being well-conditioned
at all frequencies. An implementation technique is elaborated,
where again reasonings from pseudo-differential calculus play an
important rôle. Some numerical examples are presented which appear
to confirm that the new integral equation leads to linear systems
which are much better conditioned than the classical ("direct")
integral equations and hence have much better behaviour when
solved with iterative techniques and matrix sparsification.

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